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Date May 2011 Marks available 4 Reference code 11M.2.HL.TZ2.5
Level Higher level Paper Paper 2 Time zone Time zone 2
Command term Explain Question number 5 Adapted from N/A

Question

This question is about changes of state of a gas.

A cylinder fitted with a piston contains 0.23 mol of helium gas.

The following data are available for the helium with the piston in the position shown.

      Volume = 5.2×10–3m3
      Pressure = 1.0 ×105 Pa
      Temperature = 290K

(i)   Use the data to calculate a value for the universal gas constant.
(ii)  State the assumption made in the calculation in (a)(i).
[3]
a.
The gas is now compressed isothermally by the piston so that the volume of the gas is reduced. Explain why the compression must be carried out slowly.
[2]
b.
After the compression, the gas is now allowed to expand adiabatically to its original volume. Use the first law of thermodynamics to explain whether the final temperature will be less than, equal to or greater than 290K.
[4]
c.

Markscheme

(i) use of \(R = \frac{{pV}}{{nT}}\); (award mark if correct substitution seen) 

\(\left( {\frac{{5.2 \times {{10}^{ - 3}} \times 1.0 \times {{10}^5}}}{{0.23 \times 290}}} \right) = 7.8{\rm{J}}{{\rm{K}}^{ - 1}}{\rm{mo}}{{\rm{l}}^{ - 1}}\); (accept Pa m3 mol−1 K−1 )

(ii) the gas is ideal;

a.

constant temperature required; (do not allow “isothermal”)

a slow compression allows time for (internal) energy to leave gas / OWTTE;

b.

(for adiabatic change) Q=0;
W is positive / work is done by the gas;

∆U =−W so ∆U is negative;
(T is a measure of U therefore) T less than 290K;

c.

Examiners report

(i) Very many candidates were able to arrive at a value for R from the data given. Some however fudged their answer to arrive at the accepted value of 8.31! It was common to see a unit of Pa m3 K-1 mol-1 which, while it is acceptable, shows that the candidate quoting it has little sense of the true meaning of R.

 

(ii) Most recognized that the gas has to be ideal for the calculation in (i) to be carried through.

a.
Many were able to say that the temperature must not change (isothermal). Too many simply repeated the word “isothermal” from the stem, this gained no credit. However, only a few stated with clarity that the system needs time to allow the energy to leak out to the surroundings.
b.
This part was done well, unlike similar questions in recent examinations. Candidates can explain the direction of energy flow and its consequences for the system in terms of the first law of thermodynamics. However, too many failed to use the first law and wrote in general terms about pressure and volume changes.
c.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Core topics) » B.2 – Thermodynamics
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